Scala analysis: 686_T93

  0:          1/1               0.000000 unison, perfect prime
  1:         87.500 cents      87.500000
  2:        275.000 cents     275.000000
  3:        500.000 cents     500.000000

  0:        225.0000 cents    225.0000
  1:         87.5000 cents     87.5000
  2:        187.5000 cents    187.5000
  3:        225.0000 cents    225.0000

Interval class, Number of incidences, Size:
  1:   1 87.50000 cents
  1:   1 187.50000 cents
  1:   1 225.00000 cents
  2:   1 275.00000 cents
  2:   1 312.50000 cents
  2:   1 412.50000 cents
Highest number of different intervals for one interval class: 3
Average number of different intervals per interval class: 3.00000 = 3

        1     2     3    
 0.0  : 87.5  275.0 500.0
 87.5 : 187.5 412.5 500.0
 275.0: 225.0 312.5 500.0
 500.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  87.5000   .. 225.0000 cents      137.50000 cents                    87.50000 cents
  2:  275.0000  .. 412.5000 cents      137.50000 cents                    50.00000 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 87.50000 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 225.00000 cents
Average / Smallest step             : 1.904762
Largest / Average step              : 1.350000
Largest / Smallest step             : 2.571429
Median interval of one step         : 187.50000 cents, amount: 1
Least squares average step          : 152.67857 cents, oct.:  458.03571 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 40-tone equal temperament with octave  500.000 cents
  degrees: 7 22 40
Least number of segments generator  : 21 of 262.500 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 29 of 362.500 cents and inv.
  generated superset size: 6 = 3 more = 200.000%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SML
Interval vector is [ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 50.00000 cents
Scale diversity                     : 1.100127
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.450000
Rothenberg efficiency               : 0.666667   redundancy: 0.333333
Efficiency x scale size             : 2.000000
Number of different interval sizes  : 6 = 3.00000 / class
Number of one step interval sizes   : 3
Highest interval variety            : 3
Mean interval variety               : 3.00000 = 3
Median interval variety             : 3
Lowest interval variety             : 3
Smallest interval difference        : 37.50000 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best major thirds form a closed circle
Best minor thirds form a closed circle
Steps are strictly increasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
-- Rational properties --

  3:  0 1 2   N G T3   SD: 80.3998 c. M: 108.3333 c. 
  4:  1 1 2   P M ME S SD: 26.0208 c. M:-37.5000 c. 
  5:  1 2 2  SP M ME S SD: 16.1374 c. M:-25.0000 c. 
  6:  1 2 3   P   T3   SD: 14.6329 c. M: 25.0000 c. 
  7:  1 3 3  SP M DE S SD: 11.1518 c. M: 16.0714 c. 
 11:  2 4 5  SP   T3   SD: 2.3655 c. M:-3.4091 c. 
 29:  5 11 13  SP   T3   SD: 0.8973 c. M: 1.2931 c. 
 40:  7 15 18  SP   T3   SD: 0.0000 c. M: 0.0000 c. 

 1 x x 2  S SD: 700.0000 cents
 2 x x 3  S SD: 201.9550 cents
 3 x x 4  S SD: 1.9550 cents
 4 x 5 x  S SD: 111.3137 cents
 5 x 6:7  S SD: 45.9891 cents
 6 x 7:8  S SD: 4.1804 cents
 7 x 8:9  S SD: 39.1624 cents
 8 x 9:11    SD: 43.8387 cents
 9 x 11:12    SD: 36.2172 cents
 10:11:12:13  H SD: 32.9224 cents
 11:12:13:15    SD: 24.8407 cents
 12:13:14:16  S SD: 17.2508 cents
 15:16:18:20  S SD: 15.7857 cents
 16:17:19:21    SD: 13.6026 cents
 17:18:20:23    SD: 8.9157 cents
 18:19:21:24    SD: 3.4505 cents
 41:43:48:55    SD: 3.3883 cents
 57:60:67:76    SD: 1.7929 cents
 75:79:88:100    SD: 1.1953 cents
 98:103:115:131    SD: 1.1356 cents
 99:104:116:132    SD: 1.0048 cents
 116:122:136:155    SD: 0.6074 cents
 134:141:157:179    SD: 0.5403 cents
 191:201:224:255    SD: 0.4275 cents
 215:226:252:287    SD: 0.3741 cents
 233:245:273:311    SD: 0.3040 cents
 290:305:340:387    SD: 0.2094 cents
 308:324:361:411    SD: 0.1966 cents
 406:427:476:542    SD: 0.1531 cents
 424:446:497:566    SD: 0.0384 cents